The Progress M-08M is functionally similar to the Soyuz manned vehicles, but as far as I know it does not have a reentry shield and cannot be used as a lifeboat for reentry. It's also worth noting that even if mylar-type materials are not visible, that doesn't mean they aren't
just under the surface.
However, there are post-Apollo examples of Mylar being used in manned missions, probably most famously on
Skylab:
The Skylab space station was launched just after the Apollo project ended. It was inserted into low earth orbit by one of the Saturn V launchers left over from the Apollo program. It weighed over 100 tons, easily one of the largest and heaviest objects ever orbited in one throw (along with the upper stages of Apollo).
Unfortunately, there was a problem in the final phase of deployment and the micrometeoroid shield and a solar panel were torn off, exposing some of the internal wiring of the station to potential overheating. A rather critical repair mission was sent, which needed to succeed before the wiring melted, released poison gas, and made the station uninhabitable. If humans weren't already prepared to visit (using command modules very similar to those used in the Apollo missions), the mission would have failed.
The solution? A big, ugly, wrinkled sheet of gold Mylar, clearly visible in most photographs.
Now, to doubt the authenticity of the moon landings also pretty much requires one to doubt the existence of Skylab, too, because Skylab was launched with the same kind of rocket and was visited by some of the
same people who went to the moon. Its weight alone shows that the Saturn V had more than enough ass to haul up everything a moon expedition would need (the total weight of the CSM-LM system that went to the moon was around 47000 Kg, or 50 tons, but that does not include the SV-III stage).
And of course, Skylab came back to earth, because nobody had taken into account the fact that electromagnetic fields were decaying its orbit faster than predicted, and there was a huge gap between the end of the Apollo program and the launch of the first Space Shuttle, so humans couldn't save it a second time. Many people, including me, watched it go by overhead (actually, in the southern sky) in the days before it came down, and then I subsequently saw some of the debris which was recovered in Australia.
So either it's all bullshit, or a big, big part of it is quite clearly true and entirely feasible: that we had a skyscraper-sized rocket capable of lifting enormous payloads, that we had the life support systems (built with the same 1960s-era technology and practically no computing power) which were capable of sustaining human life for at least seven times longer than the longest Apollo mission, that we had the capability to make emergency repairs and adjust mission profiles on the fly, that because of the comparatively low technology, humans were
critical to the success of the mission... and that Mylar was an important contributor to both missions!